When we add two cubes by side the resulant will be a cuboid.

length of cuboid = 2+2 = 4cm

height of cuboid = 2 cm

width of cuboid = 2 cm

Volume of new cuboid  = L * G * H = 4*2*2 = 16 cm³

To Draw Graph of  a line you need two points of line

For first equation, 2x+y =6 

y = 6 - 2x

put x = 1

y = 4

put x =2 

y =2 

For first equation,  2x-y+2=0  

y = 2x  + 2

put x = 1

y = 4

put x =2 

y =6

now  using these points draw a graph on graph paper.

Chapter-8 Quadrilaterals is an easy chapter on Geometry. There are two exercises in NCERT.

For Ex 8.1 you need to know all the basic properties of square, rectangle, parallelogram, quadrilateral, trapezium and rhombus.

For Ex 8.2 you need to understand the Mid-point theorem to solve the questions.

For the solutions, go to the Downloads section.

Also, this year the OTBA (Open Text book assessment) is from Quadrilaterals for 10 marks. Please go through that once.

Go to the Downloads section and you can download all the sample papers with their solutions. Also you can practice by giving mock tests.

To find the mode, or modal value, first put the numbers in order, then count how many of each number. A number that appears most often is the mode.

Example: 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

In order these numbers are: 3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

This makes it easy to see which numbers appear most often. In this case the mode is 23.

To find the mode, arrange the numbers in order and count how many of each number repeat itself.A number which repeats itself the most is called mode.

Half of the diameter is known as radius

r=d/ 2 

the half of the diameter is the radius

A line that crosses the centre is called diameter , line that goes from one point to another on circles circumference is called as chord.A line that touches the circle as it passes by is called as tangent.Secant is a line that passes through a circle intersecting at two points.

The diameter is the longest chord of the circle because the chord passe through the centre if circle.

Diameter is the longest chord of the circle.

Arcs of a circle which subtends equal angles at center are equal in length.

Angle in a semicircle is always right angle(90).

Angle in a semi circle is always 90

Less than method : 
First prepare a less than type cumulative frequency table.
1) On the x – axis use the upper limits of the class.
2) Mark the less than type cumulative frequency on y – axis. 
3) Plot the points using upper limits and corresponding cumulative frequencies. 
4) Join the points by a free hand curve to get ogive and to get the cumulative frequency polygon join the points by line segments. 

More than method : 
First prepare a more than type cumulative frequency table.
5) On the x – axis use the lower limits of the class.
6) Mark the more than type cumulative frequency on y – axis. 
7) Plot the points using upper limits and corresponding cumulative frequencies. 
8) Join the points by a free hand curve to get ogive and to get the cumulative frequency polygon join the points by line segments.

Less Than Ogive:- The less than cumulative frequencies are in ascending order. The cumulative frequency of each class is plotted against the upper limit of the class interval in this type of ogive and then various points are joined by straight line.

More Than Ogive:- The cumulative frequencies in this type are in the descending order. The cumulative frequency of each class is plotted against the lower limit of the class interval.

2x+5=13

2x=13-5

2x=8

x=8/2

x=4

It completely depends on person to person.

Preapre the list of your STRONG & WEAK AREAS...

Start with your strong areas first as revision of that will bulid your confidence & at the same time it will be quickest in time.

Then, you may start with the weak ones which will be kind of doubt session & needs time. Things done at the last moment during exams normally sticks well...

Number system

Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set. The cumulative frequency is calculated using a frequency distribution table, which can be constructed from stem and leaf plots or directly from the data.

π x r x 25 = 550

r = 550 x 7 /25 × 22 = 7 cm

Height = {(25)² - (7)²} = 24 cm

Volume = (1/3)πr²h

               = (1/3) × (22/7) × 7 × 7 × 24

               = 1232 cu. cm

Let the lagest number be x, then other smaller number will be (x - 50).

According to question,

6(x - 50) - 5x = 40               =>               6x - 300 - 5x = 40               =>               x = 340

Therefore, another number is 340 - 50 = 290

Thus, two numbers are 340 and 290.

Let the angles be 3x, 5x, 9x and 13x

Using angle sum property of quadrilateral,

3x + 5x + 9x + 13x = 360               =>               30x = 360               =>                x = 12

Therefore, the angles are

3x = 3 x 12 = 36^o

5x = 5 x 12 = 60^o

9x = 9 x 12 = 108^o

15x = 15 x 12 = 180^o

Let the angles be 3x ,5x,9x,13x..

Total sum =30x 

Sum of angles of quad.....=360°

It means 30x=360°

Therefore x=36°

All angles can be calculated using this

64^{1/2 =} (8²)^{1/2 =} 8 (Answer)

8

{(64)^-2}^1/4 = (64)^-2(1/4) = (64)^-1/2

               = (8)^-1 = 1/8

$\sqrt[4]{{64}^{-2}}$ = $\sqrt[4]{{\left(\frac{1}{64}\right)}^2}={\left(\frac{1}{64}\right)}^{2\times \frac{1}{4}}={\left(\frac{1}{64}\right)}^{\frac{1}{2}}$

                = $\frac{1}{8}$

Given: x/y + y/x = 1

Solution: take L.C.M which will provide (x² + y²) $/$ (xy) = 1

x² + y² = xy

x² + y² - xy = 0

Now, we know that x³ + y³ = (x + y) (x² + y² - xy)

means, x³ + y³ = (x + y)$\times$0 = 0 (Answer)

x^y = 32

taking log both sides,          log x^y = log 32

=>      log x^y = log 2^5      =>     y log x = 5 log 2    

on comapring both sides, we get         x = 2 and y = 5

thereofre,    y^x = 5^2 = 25

(x+3)^4 = x⁴ + 12x³ + 54x² + 108x + 81

therefore, the coefficients of x² on the expansion of (x+3)⁴ is 54.